EGR doesn't cool the heads.  It reduces the combustion temperature.  It's figured into the map in the ECU.  Should reduce pre ignition knocking, and changes the emissions - IIRC, it reduces NOX.

I've been running and maintaining EA82s since 1988.  Never had any noticeable effect on performance or drive ability due to EGR, or EGR solenoid failure.  The only problem I've ever had with EGR is that the OEM solenoids fail open.  I replace them with a Toyota one, still running the same Toyota ones.

The main limiter on the power output of EA82s is the air path in the intake and exhaust ports in the heads, and the valve size.  Nothing else makes much difference, unless you are prepared to spend BIG $ for small improvements.  It's less expensive to do the EJ swap if you want power, and keep the reliability.

Im no expert either but i think its just replacing oxygen that would be in the chamber.  Similar to the way running rich cools the chamber its just taking some of the volitile oxygen out and replacing it with neutral gas that has been burned already.

Also since the times it does it are light throttle cruise when timing is high, it might help curb predetonation, but thats a guess on my part.

Ya l researched it what was said made sense in way. Not able to grasp the chemistry i'll take there word tho. When l got the car it had a surge issue an gutless as hell basically carboned up an choking on it own oil l reinstalled egr after a good clean seems to work. If l can help with our impact on the planet l will. I often wonder how many times we've blown ourselves back to the stone age.